Gov. Mike Pence speaking on Tuesday in Indianapolis about a new state law that opponents say legalizes discrimination against gays and lesbians. He said the reaction took him by surprise.CreditAaron P. Bernstein/Getty Images

By turns, Gov. Mike Pence of Indiana was defiant then chastened, stern then contemplative.

After days of upheaval over a law that its supporters acclaim as ensuring religious freedom, Mr. Pence stood before reporters in the capital, Indianapolis, trying to calm the growing national storm that had, he said, taken him by surprise.

“Was I expecting this kind of backlash? Heavens no,” Mr. Pence, a Republican, said of the wave of boycotts and criticism by business, sports and political leaders, and other states over the measure that its opponents say could allow Christian conservatives to refuse to provide services to same-sex couples. “Candidly, when this erupted last week, even though I had made my position clear weeks ago that I would sign the bill, without much discussion, I was taken aback.”

Faced with what has become the most tumultuous episode of his governorship, and perhaps his political career, Mr. Pence acknowledged on Tuesday that he “could have handled” better a national television interview over the weekend in which he had awkwardly refused to answer questions about the law’s practical application, then canceled some public appearances.

Mr. Pence said he was deeply disappointed by what he termed “reckless reporting” and “gross mischaracterizations” about what the bill would do. And he spoke, emotionally at times, of his own upbringing and of what he described as the “good and decent people of Indiana,” adding, “The way I was raised was like most Hoosiers, with the golden rule.”

Mr. Pence, who has sometimes been mentioned as a Republican presidential contender, now finds himself standing uncomfortably at the center of the nation’s culture wars. He is also straddling a perilously complicated line between the moderate business wing of his party, which has objected to the law, and his social conservative base, which has embraced it.

The law itself bars government from infringing upon a person’s ability to exercise his or her faith unless the government is found to have a compelling reason to do that. But many disagree about what the law really means and how courts will interpret it.

Mr. Pence confidently announced that a change would be made to clarify that the law “does not give businesses the right to deny services to anyone.” Though he acknowledged that the change was still being drafted, he declared, “We will fix this and move forward.”

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Gov. Mike Pence, Republican of Indiana, says that the religious freedom law passed in the state was never intended to give a “license to discriminate” against gay and lesbian couples.Published OnMarch 31, 2015CreditImage by Aaron P. Bernstein/Getty Images

The promise of a change — “a clarification, but it’s also a fix,” in the words of Mr. Pence — was not enough to calm the political waters, and the fallout that might affect Mr. Pence’s political future was a question openly contemplated in the halls of the Statehouse.

State Democratic leaders demanded again on Tuesday that the law be repealed. Some conservative groups called on the Legislature to stand its ground and make no changes. Some business leaders, who had lined up against the measure, were withholding judgment on any clarification, they said, until they saw the language.

“I would not have passed this to begin with,” Richard G. Lugar, a former longtime Republican senator from Indiana, said in an interview. He added that he and three former Indianapolis mayors as well as the current mayor, Greg Ballard, also a Republican, intended to convey their concerns to Mr. Pence. Asked whether repeal would be preferable to some revision, Mr. Lugar, who was also once the mayor of Indianapolis, noted the complications.

“That’d be the cleanest way of remedying a mistake,” Mr. Lugar said, “but my guess is that a good number of the people who voted for this do not believe it is a mistake. The problem is pacifying them.”

Before being elected governor in 2012, Mr. Pence was a six-term member of the House of Representatives. He has been quoted as describing himself as “a Christian, a conservative and a Republican, in that order.” White-haired and with a strong, deep voice, he once hosted a conservative talk radio show — a level of expertise and media savvy that left some colleagues baffled by his stumbling appearance on ABC’s “This Week With George Stephanopoulos” on Sunday.

Mr. Pence refused to answer “yes or no” questions posed by Mr. Stephanopoulos over whether the measure would allow a florist to deny services to a gay couple, as its supporters maintain. “The issue here is: Is tolerance a two-way street or not?” Mr. Pence said in the interview. “There’s a lot of talk about tolerance in this country today having to do with people on the left. Here Indiana steps forward to protect the constitutional rights and privileges of freedom of religion for people of faith and families of faith in our state, and this avalanche of intolerance that’s been poured on our state is just outrageous.”

But on Tuesday he struck a different tone, praising the Rev. Dr. Martin Luther King Jr. and talking about how proud he was to walk with Representative John Lewis across the Edmund Pettus Bridge in Selma, Ala., in 2010 on the 45th anniversary of the attack on civil rights marchers there. “This issue of discrimination has been an anthem throughout my life,” Mr. Pence said.

Until now, Mr. Pence, 55, had been a relatively quiet, less-than-flashy presence as governor. Some lawmakers and political strategists said he had made few waves in Indianapolis, and been less visible in the legislative process than several of his predecessors, including Mitch Daniels, a popular Republican who left the job because of term limits.

His supporters note his efforts to cut taxes and expand charter schools. They say he has also shown flexibility on partisan issues, orchestrating changes to the state’s Medicaid system that expanded coverage to about 350,000 additional people and authorizing a needle exchange program in a rural county with an H.I.V. epidemic.

Mayor Karen Freeman-Wilson of Gary, a Democrat who described her relationship with the governor as “probably the least likely friendship in government,” praised his current efforts to find some middle ground on the religious law that she opposes.

“I think the governor has had a hard time,” Ms. Freeman-Wilson said. “I know him to be a very thoughtful person, and I think that he is really working to try to not just clarify but repair any damage that has been done to Indiana’s image.”

His critics, however, suggest that he has not made a larger mark in Indianapolis because he is simply biding his time, one eye on higher political office.

Events of the last few days, though, seem to broadly threaten Mr. Pence’s support. While at least one Democrat, Mayor Thomas M. McDermott Jr. of Hammond, went so far as to call for Mr. Pence’s resignation, even Republican legislative leaders suggested publicly that Mr. Pence could have done a better job of explaining the law. A newspaper that once endorsed him, The Indianapolis Star, took the unusual step of running a front-page editorial with giant block letters: “FIX THIS NOW.”

Political analysts in the state said Mr. Pence’s position might have, at least early on, helped him with core voters in some Republican presidential primary states if he was to run in 2016, yet his call for a “fix” on Tuesday seemed to cloud that.

“There’s no question to the extent that he harbored presidential ambitions, those are going to have to be on hold,” said Scott Pelath, the Democrats’ leader in the State House. “He has a lot of damage to repair.”

If Mr. Pence runs for re-election for governor in 2016, the episode seems likely to be a still more serious problem. Mr. Pence won statewide election in 2012 but by a margin narrower than had been seen in the state in decades.

“Whether the latest comments by him can tamp down this crisis, I’m highly skeptical,” said Brian Howey, editor of the newsletter Howey Politics Indiana. “Regular Hoosiers are aghast at what’s happened. This is a crisis and a potential disaster for Pence.”

For his part, Mr. Pence seemed to wish to declare the episode over. “It’s been a tough week here in the Hoosier state,” he said, adding firmly, “But we’re going to move forward.”

A version of this article appears in print on , on Page A14 of the New York edition with the headline: Indiana Governor, Feeling Backlash From Law’s Opponents, Promises a ‘Fix’. Order Reprints | Today’s Paper | Subscribe